1. Field of the Invention
The present invention relates to a measuring device or conversion tool which has wide applicability to the reading of scale representations, such as graphs, charts, maps and the like, independent of the scale or units used in the graph, chart or map. The present invention particularly relates to a device which can be used in the reading of scale representations by lay persons or highly skilled technical staff with ease and precision.
The device of the present invention can be considered in some formats as a ruler having universally selectable scales which can be used to measure distances with a desired linear or logarithmic scale, to draw distances to a desired scale, or to divide distances into a desired number of equal parts.
2. Background of the Art
Since the origination of graphic representations, there has always been a need for balancing the level of complexity in the representation to provide all the information that the originator feels is essential with the ease of accessing and reading that information by the widest spectrum of users of the representation. These two characteristics are not always satisfied by the same format or structure of the representation.
One of the earliest conflicts between graphic representation of information and access to users was in the field of cartography. When original globes and maps were made for the purposes of navigation, an initial difficulty was in representing a sphere as a flat surface upon which a navigator could more easily perform measurement tasks necessary for determining directions, speeds and distances necessary for a voyage. The size of the map had to be controlled, with scaling of distances for easier management of the calculations and manipulation of the graph. The scale on a map was a key in which ratios of actual measured distances on the map were related to real distances on the surface of the Earth. For example, a scale on a map might indicate that a specific distance (e.g., 1 inch) was equal to 100 miles. The unit distance on the map and the scale distance did not have to be whole integer units, but in many cases, to simplify the ability of the user to measure distances, accessible units such as 1 inch per 100 miles, etc. were selected. The map was used by a navigator, in some instances, by drawing a line on the map with a straight edge, setting a compass at the fixed unit distance (e.g., 1 inch to represent 100 miles), positioning the point of the compass at the starting point of a trip, rotating the compass from point to point (counting the number of rotations), and ceasing the rotations when an integral number of rotations has been made along the line. The last portion of the last rotation would then be determined as a fraction (e.g., there might have been 9.45 rotations). That fraction of a rotation was then converted to a fraction of the full distance (e.g., 0.45 times 100 miles) and the entire distance then estimated (e.g., 9 times 100 miles plus 0.45 times 100 miles became 945 miles). This system, combined with astronavigation, served the nautical trade adequately for many centuries, but with well known and documented limitations in its performance. With the greater accuracy in maps and navigation, and the complexities of straight-edging a line, marking up original maps, manual inaccuracies created by the drawing and compass rotation, and separate physical measurement of the fractional remains, the system is inconvenient for modern usage, even with its historical and romantic ambiance.
Much preliminary technical work, at the workplace, in estimations, and planning, requires the use of scaled representations in its performance. Similarly, much drafting work in architecture, estimating graph readings in chemical engineering, planning in agriculture, and other fields, requires quick access and conversion of graphs and charts to usable information, without further diminishing of the numerical accuracy of the reading by manual error or complexity.
Conventional rulers contain only a limited number of scales, which are usually selected from the standard series of metric scales, architect scales, or engineer scales. The ruler in U.S. Pat. No. 4,707,928 to Bennett et. al. entitled VARI-SCALE, for example, contains seventeen of the above mentioned scales. A disadvantage of conventional rulers is that the selections of scales are limited to a finite number, say, 17. The consequence is that when a measurement requires a scale other than a conventional scale, the measurement with a conventional ruler becomes difficult and time-consuming. For example, distances on a map or a technical graph are usually predefined by a so-called reference scale which was used to create the map or graph. To measure distances on such a map or a graph, the best way is to use this reference scale directly. With a conventional ruler, however, the distances must be first measured with a standard scale which is, in general, different from the reference scale, and then the reference scale must also be measured with the same standard scale. Third, a conversion relationship between these two different scales must be established, which requires certain mathematical knowledge. Finally, the conversion must be physically carried out, in more difficult cases, by a calculator, and in easier cases, by mental calculation.
Another disadvantage of conventional rulers is that conventional rulers contain only linear scales without logarithmic scales. When a logarithmic type of distance, which usually occurs in a logarithmic type of graph, needed to be measured, the conversion between a linear scale and a logarithmic scale must be conducted. This type of conversion is far more troublesome than a conversion between two linear scales.
A further disadvantage of conventional rulers is to use them to draw distances to a scale not contained in conventional rulers. The conversions between different scales and calculations by a calculator are inevitable.
An additional disadvantage of the conventional rulers is the inability or difficulty in using them to divide a distance or a primary line into an optional number of equal parts. It usually involves dimensional measurement, division and multiplication by a calculator. The ruler means in U.S. Pat. No. 4,208,804 to Lundin titled RULER MEANS FOR DIVIDING A DISTANCE offers an alternative method for doing this but the measurement process with the ruler means is relatively complicated. Moreover, dividing a distance is the only task it performs. To divide a distance or a primary line into equal parts, a rotating arm is placed at a 0,0 axis. A line to an X axis is dropped (by drawing with a straight edge) from the point or end point of the distance or primary line to be divided. The rotating arm is rotated so that the end distal from the 0,0 axis intersects the particular number selected for the number of segments. The rotating arm contains numbers (e.g., 0, 1, 2, 3, 4, . . . . ), and these numbers indicate the position of the cutting lines of the distance or primary line. Secondary lines must be straight-edge drawn to the X axis from the cutting points of the numbers on the rotating arm. These cutting lines are then extended up to the primary line or a working line drawn from the Y axis to the point. These cutting lines then define the segments created in dividing the line or distance into the predetermined number of parts. As can be seen, a significant amount of straight edge work and multiple line drawing must be done. This is complex and introduces significant possibilities for error introduction and lack of precision.
U.S. Pat. No. 4,736,526 to Hsia, titled GEOMETRY TEMPLATE discloses an apparatus in which a clear plastic template bears a combination of inscribed marks and apertures to cooperate with each other to facilitate drawing of common geometric figures. An annexed arm is shown which is attached in an axial manner to a portion of the template so that it may rotate. The annexed arm has numerous holes in it to assist in drawing circles.
U.S. Pat. No. 3,507,045 to Rives, titled RULE WITH INTERCHANGEABLE SCALES discloses a support body into or onto which a plurality of scales may be interchanged. Different scales are attached to the ruler support body for preselected uses.
Other physical structures in ruler form which have premarkings, slots, holes and the like for accurately locating portions of a distance or relative positions include U.S. Pat. No. 4,750,270 to Kundlikoff, titled MEASURING RULER; U.S. Pat. No. 5,847,223 to Krane, titled LINEAR SCALE; and U.S. Pat. No. 5,058,285 to Morita et al., titled TEMPLATE.
U.S. Pat. No. 4,625,425 to Senno et al., titled UNIVERSAL TRIANGLE describes a drafting implement consisting of an interchangeable circular triangle and circular disk, each being imprinted and having measurement and drafting aids to make technical drawings and measurements. Individual disks or templates are inserted for each type of drawing or measurement to be made.